Typically, a global positioning system (GPS) can provide a user with a position, velocity, and time (PVT) solution, sometimes referred to as a navigation solution. The global positioning system includes a GPS receiver which typically incorporates current measurements from four or more satellites to update its most recent PVT solution. The navigation solution includes pseudorange, which can be referred to as a first-approximation measurement for the distance between a satellite and a navigation receiver, such as, for example, global positioning system (GPS) receivers. To determine a receiver position, a navigation receiver typically determines the ranges to (at least) three satellites as well as their positions at the time of transmitting. The satellites positions can be calculated for any point in time with known satellite orbital parameters, which specify that satellites' orbits are represented by way of a model of two point masses obeying the Newtonian laws of motion and the inverse-square law of gravitational attraction.
The pseudoranges can be computed using measured time that the navigation receiver receives signals from the satellite, multiplied by the speed of light. To measure this time, the relationship between the internal receiver time and GPS time is typically known. This is done by introducing the receiver clock offset Δt into the positional computation, utilizing at least one extra satellite signal. With four signals, solutions for the receiver position along the x-, y-, z- and Δt-axes can be computed.
The reason for pseudoranges rather than actual ranges is a result of uncertain receiver clock offset, among others. Typically, if the pseudoranges increase with larger uncertainties, the computation of the receiver position becomes less accurate. Thus, a heretofore unaddressed need exists in the industry for computing an accurate receiver position tolerant to uncertainties.